Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems

TL;DR

This paper introduces a comprehensive hierarchy of criteria for detecting EPR steering in bipartite quantum systems, including continuous variables, enabling optimal and experimentally feasible steering witnesses with higher loss tolerance.

Contribution

It develops a systematic framework for deriving nonlinear steering criteria and optimal witnesses applicable to all bipartite quantum states, including multipartite scenarios.

Findings

Recovered known steering criteria as special cases

Derived an optimal steering witness for a lossy single-photon Bell state

Demonstrated higher loss tolerance than existing methods

Abstract

Einstein-Podolsky-Rosen steering is a manifestation of quantum correlations exhibited by quantum systems, that allows for entanglement certification when one of the subsystems is not characterized. Detecting steerability of quantum states is essential to assess their suitability for quantum information protocols with partially trusted devices. We provide a hierarchy of sufficient conditions for the steerability of bipartite quantum states of any dimension, including continuous variable states. Previously known steering criteria are recovered as special cases of our approach. The proposed method allows us to derive optimal steering witnesses for arbitrary families of quantum states, and provides a systematic framework to analytically derive non-linear steering criteria. We discuss relevant examples and, in particular, provide an optimal steering witness for a lossy single-photon Bell state; the witness can be implemented just by linear optics and homodyne detection, and detects steering with a higher loss tolerance than any other known method. Our approach is readily applicable to multipartite steering detection and to the characterization of joint measurability.